I would glue some rubber pads on the bottom of the toilet seat, that should do it.
While the toilet seat slamming down may not be that bad in terms of decibels, it might be amplified by one's bathroom, especially assuming the door was closed. All that hard tile, porcelain sink and tub, etc make for a perfect storm of reflective noise. There is nothing soft that might absorb the sound except maybe a towel, a roll of toilet paper and the human that is in there. My guess is the human would be the primary sound absorber, even if they had Charmin TP.